I chose the Student of Archery background for a druid and it appears that it does not grant the martial->simple proficiency for the composite longbow (my choice of weapon). The edit feature allows it to be modified, but that shouldn’t be necessary.
“Choose a ranged weapon (subject to GM approval). For the purposes of proficiency, ** if your choice is a martial weapon, you treat it as a simple weapon**; if it’s an advanced weapon, you treat it as a martial weapon. With this weapon, you ignore the penalty for making ranged attacks within your second range increment, and at 5th level, whenever you get a critical hit with this weapon, you get its critical specialization effect.”